Zbirka rijesenih zadataka - PBF - Sveučilište u Zagrebu
Zbirka rijesenih zadataka - PBF - Sveučilište u Zagrebu
Zbirka rijesenih zadataka - PBF - Sveučilište u Zagrebu
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Ž. Kurtanjek: <strong>PBF</strong> Mjerenja i automatizacija 2007/2008 32<br />
17.<br />
s<br />
2<br />
ω<br />
n<br />
+ 2⋅ξ ⋅ω<br />
⋅ s + ω<br />
2 2<br />
n n<br />
1 −ξ⋅ω<br />
n⋅t<br />
⋅ω<br />
⋅e<br />
⋅sin<br />
2<br />
n<br />
n<br />
z<br />
( ω ⋅ z⋅t) z = 1−ξ<br />
ξ < 1<br />
26.<br />
s<br />
2<br />
ω<br />
n<br />
⋅ s<br />
2 ξ ω s<br />
n −ξ<br />
⋅ω<br />
n⋅t<br />
( )<br />
+ ⋅ ⋅ ⋅ +<br />
⋅e<br />
⋅sin<br />
ωn<br />
⋅ z ⋅t<br />
+ Φ<br />
ω<br />
2 2<br />
n n<br />
2<br />
ω<br />
ξ < 1<br />
z<br />
⎛ ⎞<br />
= −<br />
2<br />
z<br />
z 1 ξ Φ = arctan⎜<br />
− ⎟<br />
⎝ ξ ⎠<br />
Izraz za Y(s) napišemo u skladu s formulama 17 i 26 na slijedeći način:<br />
Y<br />
( s)<br />
= 0,5 ⋅<br />
s<br />
2<br />
1<br />
+ 0,5 ⋅<br />
3<br />
+ ⋅ s + 1 s<br />
2<br />
2<br />
s<br />
3<br />
+ ⋅ s + 1<br />
2<br />
3 9 1<br />
Usporedbom dobijemo ω n<br />
= 1 ξ = z = 1−<br />
= ⋅ 7<br />
4 16 4<br />
Uvrštavanjem dobije se konačni izraz:<br />
y<br />
( t)<br />
3<br />
1 − ⋅t<br />
4<br />
= ⋅ e<br />
14<br />
⎛ ⎛<br />
⋅ ⎜7<br />
⋅ cos⎜<br />
⎝ ⎝<br />
7 ⎞<br />
⋅t<br />
⎟<br />
+<br />
4 ⎠<br />
⎛<br />
7 ⋅sin⎜<br />
⎝<br />
7 ⎞⎞<br />
⋅ t ⎟⎟<br />
4<br />
⎠⎠<br />
Rezultat možemo prikazati grafički (uporabom računalne podrške, npr. W.R.<br />
Mathematica ili Matlab.<br />
0.5<br />
y(t)<br />
0.4<br />
0.3<br />
0.2<br />
0.1<br />
2 4 6 8 10<br />
t
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